On Asymptotes and Matter:

Required reading: Asymptotes, On Events, On the paradox of infinite divisibility

"Approaching zero" refers to a mathematical concept involving parabolas and curves. An asymptote is a theoretical line which the curve always approaches, but never intersects with, such that if the line were to have a value of zero*, the curve would always approach, but never reach it. Similarly, nearly every quality or attribute has the capacity to “approach zero,” but never reach it.

Asymptotes in parabolic mathematics are examples of how infinite divisibility is a universal trait in a real-world context. The curve never reaches zero because it is dividing the space between the two infinitely. Metaphorically speaking, human experience is the curve, while exact time or exact location is the asymptote. Our curve of experience naturally approaches an exact time or an exact space, but never meets it.

The asymptotic nature of matter (and time) in conjunction with infinite divisibility necessitates that no one particle of matter (or time) can be truly pinpointed. The problem is that it appears as though experience approaches empirical (or objective) reality, but never reaches it. The evidence of reality is made so transitory by its divisibility. The result is that existence and infinite divisibility seem to imply non-existence by the impossibility of making true “this object exists at location x at time t.” This is to say that events/objects cannot be said to exist, because they lack modifiers.

All matter in the universe appears to be on the threshold of being real. Could this be the scientific application of idealism or immaterialism? We're angling dangerously toward hippie talk, here.

*In this case, "zero" refers to the distance of the parabola from the asymptote (or of the curve of existence from reality), and not an absence of value or substance.



Next time: On time and eternal recurrence, in which I try to espouse one of the most important Nietzschean concepts that I don't actually believe.

On Simultaneity:

Required Reading: Simultaneity, Relativity of simultaneity, the present, the paradox of infinite divisibility

I'd like to note, before I get down to business that the wikipedia page for simultaneity has an interesting point, which is that the root of the word "simultaneous" - simult - is indicative of a supernatural or divine coincidence. Understand, as you read the rest of this entry, just how supernatural a coincidence it would have to be for two events to occur simultaneously. Thought for food.

Simultaneity is improbable for the same reasons that pinpointing “the present” is impossible. I say improbable, because it is possible that two events could occur at the exact same time - no matter how infinitely small the increments of time-measurement are.

However, the smaller the measurements are (and remember, the increments of measurement could become infinitely smaller) the more likely it is that you'll discover that two events that appear to be simultaneous are in fact set apart by such and such an infinitely small duration. So, simultaneous events are extremely rare, to the point that it is likely that they have either never occurred or will never occur.

That said it is possible for events in progress to be happening simultaneously, provided that the "happening" of the event is described in a nonspecific way. For example, “burning” refers to the process of being burnt, but does not refer to any specific part of that process. So, two candles can be burning simultaneously, but it can't be determined by any accurate means whether they were lit simultaneously, or burnt out simultaneously, or put out simultaneously, or reached the middle of the candle simultaneously, or began to melt simultaneously, etc.

Because the occurrence of events is asymptotic (approaching zero or infinity), we have to assume (again) that it is either impossible to determine simultaneity, or it must be the case that simultaneity itself is not possible.

Just like we need relative durations in order to talk about the present, we need to think of occurrences relatively in order to assume that some of them happen simultaneously. Without turning a blind eye to the indeterminacy that's packaged in with these concepts, we would lack the ability to experience or comprehend time in a stable and cohesive sort of way.

Meanwhile simultaneity as an objective concept cannot be considered a true possibility - rather, a theoretical concept.

Next week: On the infinite, in which I tackle infinite divisibility a little more directly and try to explain what it really means for something to be infinite.